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Number Theory: Structures, Examples, and Problems

Number Theory: A Problem-Solving Approach

Penned By Titu Andreescu
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Number Theory: Structures, Examples, and Problems

Number Theory: A Problem-Solving Approach

Penned By Titu Andreescu
4.85 54,327 Ratings
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Editor's Note:
This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.

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Length N/A Pages
Released October, 2006
Identifier (ISBN) 1484781
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Titu Andreescu
The Mind Behind the Work
Titu Andreescu

Titu Andreescu is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Titu Andreescu can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Christopher Gonzalez January 16, 2025
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author."
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"Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
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Steven Collins
Steven Collins September 03, 2025
"Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
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"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
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"Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author."
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"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem."
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"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
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"Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author."
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"Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author."
Donald Reyes
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"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
Rebecca Roberts
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"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece."
Gary  Davis
Gary Davis September 07, 2024
"A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Cynthia Moore
Cynthia Moore March 05, 2025
"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
Mark Phillips
Mark Phillips March 10, 2025
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
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"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
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"Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
Barbara Carter
Barbara Carter November 19, 2024
"I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece."
Lisa Flores
Lisa Flores January 04, 2025
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece."
Matthew Wilson
Matthew Wilson December 12, 2024
"I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Dorothy Hall
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"Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Eric Clark
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"I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend."
Emily Campbell
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"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall."
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Stephanie Brown May 01, 2024
"Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem."
Matthew Edwards
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"Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars."
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"I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes."
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Edward Lee
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"Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading."
Ashley Campbell
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"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me."
Kevin Thompson
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"A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars."
Michelle Garcia
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"Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
William Young
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Matthew Phillips
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"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
George Thompson
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers."
Christopher Phillips
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"I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend."
Christopher Miller
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"Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
Robert Garcia
Robert Garcia August 17, 2024
"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend."
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"A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
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"A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading."
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"Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me."
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"Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author."
Ryan Smith
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"Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend."
Karen Baker
Karen Baker January 27, 2024
"A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel."
Amanda Diaz
Amanda Diaz March 18, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars."
Kevin Taylor
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"I find myself somewhat conflicted. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time."
Elizabeth Wilson
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"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
Gary Lewis
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"Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall."
Rebecca Roberts
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"I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars."
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Deborah Flores December 07, 2025
"I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars."
Laura Adams
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"A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading."
Edward Ramirez
Edward Ramirez July 04, 2025
"I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers."
Amanda Phillips
Amanda Phillips September 03, 2025
"Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre."
Betty Evans
Betty Evans August 15, 2025
"An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars."
Amanda Phillips
Amanda Phillips December 01, 2025
"Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre."
Amanda Diaz
Amanda Diaz August 17, 2024
"Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem."
Jessica Brown
Jessica Brown August 08, 2025
"I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend."
George  Parker
George Parker May 19, 2025
"I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
Joseph Flores
Joseph Flores June 14, 2025
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars."
Matthew Baker
Matthew Baker December 01, 2024
"An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars."
Kevin Nguyen
Kevin Nguyen March 30, 2025
"Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem."
Cynthia Collins
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"Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars."
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"A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre."
Barbara Carter
Barbara Carter June 29, 2024
"A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall."
Mark Wilson
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"Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading."
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